Note that in the absence of external inputs, the populations of both emitters should fall to zero rapidly and the nonreciprocal phenomenon can only be observed within a short-lived duration, as shown in Figs. REF  and REF . It has been shown that giant atoms (self-interference resonators) can be completely decoupled from the waveguide and thus no longer emit photons to it [1]}, [2]}, [3]}. However, this generally makes the emitters isolated such that they can hardly interact with each other if they are spatially separated. Thanks to the braided structure proposed in Refs. [1]}, [2]}, decoherence-free couplings can be achieved between far apart giant atoms, i.e., the spontaneous emissions of the atoms to the waveguide can be completely suppressed while the indirect coupling between them is nonvanishing. Nevertheless, we would like to point out that a dimer model with such a braided structure is unable to demonstrate nonreciprocal transfer, although the lifetime of the emitter can be markedly extended in this case (see more details in Appendix ).
